Introduction to Complex Analytic Geometry
Authors
Description
This book is designed to be of interest to graduate students. The various topics have been presented in as elementary and self-contained a manner as possible. The theory and concepts are illustrated with numerous examples and exercises, and solutions to the exercises are given at the end of the book.
The book covers the notion of analytic function of several complex variables and some basic properties are given; fundamental extension theorems of analytic functions and notions of holomorphy domain; the study of analytic sets; the germs of analytic sets; analytic applications between analytic sets; and essential singularities.
The presentation is detailed, trying to make it easier for self-taught students.
Target audience
Higher education
Name: Introduction to Complex Analytic Geometry
Author(s): e Marcos Sebastiani
Pages: 265
Publication: IMPA, 2010
ISBN: 978-85-244-0218-0
Edition: 2
Introduction
Notations
I Preliminaries and Basic Concepts
1 Holomorphic applications
2 First properties
3 The inverse application theorem
4 Complex analytic varieties
5 Groats of holomorphic functions
6 Analytic coverings
7 Meromorphic functions
8 Topological complements
II Exercises on Analytic Functions
1 Extension of limited functions
2 Extension of any function
3 Domains of holomorphy
III Preparation Theorem and Applications
1 Sets defined by an equation
2 The preparation theorem
3 The division theorem
4 Analytic sets
5 Local parameterization of analytic sets
IV Local Properties of Analytic Sets
1 Reducible and irreducible germs
2 Dimension
3 Local rings. Singular and regular points
V Analytical applications
1 Analytical applications
2 Maximum principle
3 Extension of analytical functions
4 Eigenimages of analytical sets
5 Analytical applications of finite type
6 Multiplicities
7 Complete intersections
VI Essential Singularities
1 Global decomposition of analytic sets
2 Extension in the case of different dimensions
3 Algebraic sets
4 Extension in the case of equal dimensions
Appendix I
1 Noetherian rings
2 Idea radicals
3 Integer extensions
4 Primitive elements
5 Discriminant
Appendix II
1 Eigenimages of analytic sets
2 Tangent cone
Indicators for Solving the Exercises
Bibliography
Analytical Index